We now compare our MPMF method with several state-of-the-art imbalanced learning algorithms,
including the over-sampling methods: Random Over-Sampling (ROS) [1]},
Synthetic Minority Over-Sampling TEchnique (SMOTE) [2]},
ADAptive SYNthetic sampling (ADASYN) [3]}), the under-sampling methods:
Random Under-Sampling (RUS) [1]}, Cluster Centroids (CC) [5]},
and the ensemble learning methods: Balanced Random Forest Classifier (BRF) [6]}
and RUSBoost [7]}.
These compared algorithms are implemented with the help of an open-source toolbox Imbalanced-learn [5]}
and the package Scikit-learn [9]}.
For the resampling methods, we train a linear SVM on the new datasets.
Noting that the ensemble methods learn a nonlinear classifier, we also train a KMPMF model.
For computational effectiveness, we randomly choose 200 positive samples and 200 negative samples
as the kernel support vectors, respectively (for the dataset Breast, we choose 100 positive samples
and 100 negative samples). Table REF  gives the running time (in seconds) of
the algorithms used for imbalanced classification problems.
In most cases, MPMF is faster than the compared imbalanced learning algorithms, especially for large-scale datasets.
This means that this new method MPMF scales well to deal with large-scale imbalanced claffication problems.
Table REF  presents the obtained values of the F1-measure.
From the experimental results, it can be seen that our linear MPMF model has a better performance than
the compared resampling methods and our nonlinear model KMPMF achieves a comparable result for the F1-measure
with the compared ensemble methods.
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